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Cooperation in alternating interactions with memory constraints

Author

Listed:
  • Peter S. Park

    (Harvard University)

  • Martin A. Nowak

    (Harvard University
    Harvard University)

  • Christian Hilbe

    (Max Planck Institute for Evolutionary Biology)

Abstract

In repeated social interactions, individuals often employ reciprocal strategies to maintain cooperation. To explore the emergence of reciprocity, many theoretical models assume synchronized decision making. In each round, individuals decide simultaneously whether to cooperate or not. Yet many manifestations of reciprocity in nature are asynchronous. Individuals provide help at one time and receive help at another. Here, we explore such alternating games in which players take turns. We mathematically characterize all Nash equilibria among memory-one strategies. Moreover, we use evolutionary simulations to explore various model extensions, exploring the effect of discounted games, irregular alternation patterns, and higher memory. In all cases, we observe that mutual cooperation still evolves for a wide range of parameter values. However, compared to simultaneous games, alternating games require different strategies to maintain cooperation in noisy environments. Moreover, none of the respective strategies are evolutionarily stable.

Suggested Citation

  • Peter S. Park & Martin A. Nowak & Christian Hilbe, 2022. "Cooperation in alternating interactions with memory constraints," Nature Communications, Nature, vol. 13(1), pages 1-11, December.
    • Handle: RePEc:nat:natcom:v:13:y:2022:i:1:d:10.1038_s41467-022-28336-2
    DOI: 10.1038/s41467-022-28336-2
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    References listed on IDEAS

    as
    1. Zhang, Huanren, 2018. "Errors can increase cooperation in finite populations," Games and Economic Behavior, Elsevier, vol. 107(C), pages 203-219.
    2. Ethan Akin, 2015. "What You Gotta Know to Play Good in the Iterated Prisoner’s Dilemma," Games, MDPI, vol. 6(3), pages 1-16, June.
    3. Matthew O. Jackson & Tomas Rodriguez-Barraquer & Xu Tan, 2012. "Social Capital and Social Quilts: Network Patterns of Favor Exchange," American Economic Review, American Economic Association, vol. 102(5), pages 1857-1897, August.
    4. Alexander J. Stewart & Joshua B. Plotkin, 2015. "The Evolvability of Cooperation under Local and Non-Local Mutations," Games, MDPI, vol. 6(3), pages 1-20, July.
    5. Fudenberg, Drew & Imhof, Lorens A., 2006. "Imitation processes with small mutations," Journal of Economic Theory, Elsevier, vol. 131(1), pages 251-262, November.
    6. Kate Donahue & Oliver P. Hauser & Martin A. Nowak & Christian Hilbe, 2020. "Evolving cooperation in multichannel games," Nature Communications, Nature, vol. 11(1), pages 1-9, December.
    7. García, Julián & van Veelen, Matthijs, 2016. "In and out of equilibrium I: Evolution of strategies in repeated games with discounting," Journal of Economic Theory, Elsevier, vol. 161(C), pages 161-189.
    8. Martin A. Nowak & Akira Sasaki & Christine Taylor & Drew Fudenberg, 2004. "Emergence of cooperation and evolutionary stability in finite populations," Nature, Nature, vol. 428(6983), pages 646-650, April.
    9. Christian Hilbe & Krishnendu Chatterjee & Martin A. Nowak, 2018. "Publisher Correction: Partners and rivals in direct reciprocity," Nature Human Behaviour, Nature, vol. 2(7), pages 523-523, July.
    10. Christian Hilbe & Krishnendu Chatterjee & Martin A. Nowak, 2018. "Partners and rivals in direct reciprocity," Nature Human Behaviour, Nature, vol. 2(7), pages 469-477, July.
    11. Christian Hilbe & Kristin Hagel & Manfred Milinski, 2016. "Asymmetric Power Boosts Extortion in an Economic Experiment," PLOS ONE, Public Library of Science, vol. 11(10), pages 1-14, October.
    12. M.C. Boerlijst & M.A. Nowak & K. Sigmund, 1997. "Equal Pay for all Prisoners/ The Logic of Contrition," Working Papers ir97073, International Institute for Applied Systems Analysis.
    13. Benjamin M Zagorsky & Johannes G Reiter & Krishnendu Chatterjee & Martin A Nowak, 2013. "Forgiver Triumphs in Alternating Prisoner's Dilemma," PLOS ONE, Public Library of Science, vol. 8(12), pages 1-8, December.
    14. Julián García & Arne Traulsen, 2012. "The Structure of Mutations and the Evolution of Cooperation," PLOS ONE, Public Library of Science, vol. 7(4), pages 1-9, April.
    15. Hilbe, Christian & Traulsen, Arne & Sigmund, Karl, 2015. "Partners or rivals? Strategies for the iterated prisoner's dilemma," Games and Economic Behavior, Elsevier, vol. 92(C), pages 41-52.
    16. B. Douglas Bernheim & Michael D. Whinston, 1990. "Multimarket Contact and Collusive Behavior," RAND Journal of Economics, The RAND Corporation, vol. 21(1), pages 1-26, Spring.
    17. Johannes G. Reiter & Christian Hilbe & David G. Rand & Krishnendu Chatterjee & Martin A. Nowak, 2018. "Crosstalk in concurrent repeated games impedes direct reciprocity and requires stronger levels of forgiveness," Nature Communications, Nature, vol. 9(1), pages 1-8, December.
    18. Nikoleta E. Glynatsi & Vincent A. Knight, 2021. "A bibliometric study of research topics, collaboration, and centrality in the iterated prisoner’s dilemma," Palgrave Communications, Palgrave Macmillan, vol. 8(1), pages 1-12, December.
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    2. Noblit, Graham Alexander & Henrich, Joseph, 2023. "The Evolution of Ostracism in Human Societies," SocArXiv z3gs7, Center for Open Science.

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